Precalculus

Knowledge and Skills Required

Depending on your institution's policy, a passing score on the exam can:

Show your college math professors that you're ready for a calculus class

Allow you to opt out of a math proficiency core requirement

Earn you three college credits

The Precalculus examination assesses student mastery of skills and concepts required for success in a first-semester calculus course. A large portion of the exam is devoted to testing a student's understanding of functions and their properties. Many of the questions test a student's knowledge of specific properties of the following types of functions: linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined. Questions on the exam will present these types of functions symbolically, graphically, verbally, or in tabular form. A solid understanding of these types of functions is at the core of all precalculus courses, and it is a prerequisite for enrolling in calculus and other college-level mathematics courses.

The examination contains approximately 48 questions, in two sections, to be answered in 90 minutes. Any time candidates spend on tutorials and providing personal information is in addition to the actual testing time.

Section 1: 25 questions, 50 minutes.
The use of an online graphing calculator (non-CAS) is allowed for this section. Only some of the questions will require the use of the calculator.

Section 2: 23 questions, 40 minutes.
No calculator is allowed for this section.

Although most of the questions on the exam are multiple-choice, there are some questions that require students to enter a numerical answer.

Graphing Calculator

A graphing calculator, the TI-84 Plus CE, is integrated into the exam software, and available to students during Section 1 of the exam. Only some of the questions actually require the graphing calculator.

Information about the graphing calculator, including opportunities to practice, is available here.

In order to answer some of the questions in the calculator section of the exam, students may be required to use the online graphing calculator in the following ways:

Functions: Concept, Properties, and Operations (15%)

Ability to demonstrate an understanding of the concept of a function, the general properties of functions (e.g., domain, range), function notation, and to perform symbolic operations with functions (e.g., evaluation, inverse functions)

Representations of Functions: Symbolic, Graphical, and Tabular (30%)

Ability to recognize and perform operations and transformations on functions presented symbolically, graphically, or in tabular form

Ability to demonstrate an understanding of basic properties of functions and to recognize elementary functions (linear, quadratic, absolute value, square root, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions) that are presented symbolically, graphically, or in tabular form

Analytic Geometry (10%)

Ability to demonstrate an understanding of the analytic geometry of lines, circles, parabolas, ellipses, and hyperbolas

Trigonometry and its Applications* (15%)

Ability to demonstrate an understanding of the basic trigonometric functions and their inverses and to apply the basic trigonometric ratios and identities (in right triangles and on the unit circle)

Ability to apply trigonometry in various problem-solving contexts

Functions as Models (10%)

Ability to interpret and construct functions as models and to translate ideas among symbolic, graphical, tabular, and verbal representations of functions

* Note that trigonometry permeates most of the major topics and accounts for more than 15% of the exam. The actual proportion of exam questions that requires knowledge of either right triangle trigonometry or the properties of the trigonometric functions is approximately 30%–40%.

Study Resources

Most textbooks used in college-level precalculus courses cover the topics in the outline given earlier, but the approaches to certain topics and the emphases given to them may differ. To prepare for the Precalculus exam, it is advisable to study one or more college textbooks, which can be found in most college bookstores. When selecting a textbook, check the table of contents against the knowledge and skills required for this test.

Textbooks

A survey conducted by CLEP found that the following textbooks are among those used by college faculty who teach the equivalent course. You might purchase one or more of these online or at your local college bookstore.

Online Resources

These resources, compiled by the CLEP test development committee and staff members, may help you study for your exam. However, none of these sources are designed specifically to provide preparation for a CLEP exam. The College Board has no control over their content and cannot vouch for accuracy.

Score Information

Each institution reserves the right to set its own credit-granting policy, which may differ from that of ACE. Contact your college as soon as possible to find out the score it requires to grant credit, the number of credit hours granted, and the course(s) that can be bypassed with a satisfactory score.

*The American Council on Education’s College Credit Recommendation Service (ACE CREDIT) has evaluated CLEP processes and procedures for developing, administering, and scoring the exams. The score listed above is equivalent to a grade of C in the corresponding course. The American Council on Education, the major coordinating body for all the nation’s higher education institutions, seeks to provide leadership and a unifying voice on key higher education issues and to influence public policy through advocacy, research, and program initiatives. Visit the ACE CREDIT website for more information.